Energy Efficiency of a Wheeled Bio-Inspired Hexapod Walking Robot in Sloping Terrain

Citation: Žák, M.; Rozman, J.; Zboˇril, F.V. Energy Efficiency of a Wheeled Bio-Inspired Hexapod Walking Robot in Sloping Terrain. Robotics 2023,12, 42. https://doi.org/10.3390/ robotics12020042 Academic Editor: Dan Zhang Received: 7 February 2023 Revised: 10 March 2023 Accepted: 13 March 2023 Published: 15 March 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). robotics Article Energy Efficiency of a Wheeled Bio-Inspired Hexapod Walking Robot in Sloping Terrain Marek Žák *, Jaroslav Rozman and František V. Zboˇril Department of Intelligent Systems, Faculty of Information Technology, Brno University of Technology, Božetˇechova 2, 612 66 Brno, Czech Republic *Correspondence: izakmar[email protected].cz Abstract: Multi-legged robots, such as hexapods, have great potential to navigate challenging terrain. However, their design and control are usually much more complex and energy-demanding compared to wheeled robots. This paper presents a wheeled six-legged robot with five degrees of freedom, that is able to move on a flat surface using wheels and switch to gait in rugged terrain, which reduces energy consumption. The novel joint configuration mimics the structure of insect limbs and allows our robot to overcome difficult terrain. The wheels reduce energy consumption when moving on flat terrain and the trochanter joint reduces energy consumption when moving on slopes, extending the operating time and range of the robot. The results of experiments on sloping terrain are presented. It was confirmed that the use of the trochanter joint can lead to a reduction in energy consumption when moving in sloping terrain. Keywords: bio-inspired hexapod; six-legged robot; robot energy efficiency 1. Introduction Legged robots are well suited to navigate rugged terrain. Although they are more complex to operate than wheeled or tracked robots, new walking robots of different shapes and sizes are being designed. As the number of limbs increases, the stability and number of gaits of the robot also increases. The greatest improvement is observed between fourand six-legged robots [ 1 ]. Walking robots can be statically or dynamically stable and can move by walking, running, jumping or climbing. The most common statically stable legged robots are hexapods. With six limbs, they can move using many different gaits. Many hexapods have only three degrees of freedom per limb, so they can only affect the position of foot tip; namely MAX [ 2 ], AMOS II [ 3 ], Messor-II [ 4 ], DLR-Crawler [ 5 ] or HECTOR [ 6 ]. However, four or more degrees of freedom per leg increases the number of possible robot stances. ASTERISK [ 7 ], or Lauron V [ 8 ], has four degrees of freedom per leg and Weaver, a proprioceptive-controlled hexapod, has five degrees of freedom per leg [ 9 ]. Besides the number of degrees of freedom of the limb, the arrangement of the individual joints is also important as it determines the range of movement of the limb. The coxa link in most of the listed robots is the shortest limb link. Femur and tibia links should be of similar length. However, this is not the case with the DLR-Crawler, which has a femur link almost twice as long as the tibia link, and the AMOS II and MAX, which have tibia links almost twice as long as femur links (see Table 1). Many researchers are also trying to mimic the structure, or behavior, of insects in order to make legged robots move more efficiently, e.g. Abigaille-III [ 10 ]—a climbing hexapod, RHex, and its successor X-RHex—biologically inspired hexapod runners [ 11 , 12 ], or hexapods with distributed control and local leg reflexes [13]. Despite the considerable advantages of legged robots, their deployment in real-world missions is not very common. Hexapod robots are able to move in very difficult terrain, some can also move in sloping terrain, but at the expense of speed and higher energy Robotics 2023,12, 42. https://doi.org/10.3390/robotics12020042 https://www.mdpi.com/journal/robotics Robotics 2023,12, 42 2 of 15 consumption. By using a limb with only one controlled joint and a rugged body design [ 11 ], the robustness of the robot and lowered energy consumption during movement can be achieved, but at the cost of ability to control the position of the foot tip in difficult terrain. A higher number of degrees of freedom of the limb increases the manoeuvrability of the robot and its limbs. However, a higher number of motors also increases the weight and energy consumption of the robot. Table 1. Comparison of legged robots. Robot Leg DOF Dimensions Mass Speed †Coxa Trochanter Femur Tibia Tarsus L×W×H [kg] [m/s] [m] [m] [m] [m] [m] MAX 3 2.4 ×2.1 ×2.3 60.0 0.08 0.8 1.5 AMOS II 3 0.5 ×0.4 ×0.1 4.2 0.035 0.06 0.115 Messor II 3 0.5 ×0.5 ×0.2 2.6 DLR-Crawler 4 0.5 ×0.5 ×0.2 3.5 0.20 0‡0.075 0.04 0.04 Hector 3 13.0 0.032 0.26 0.28 ASTERISK 4 4.0 0.07 0.05 0.105 0.105 Lauron V 4 0.9 ×0.8 ×0.7 43.5 0.14 Weaver 5 0.6 ×0.6 ×0.3 7.0 0.12 0.067 0.062 0.107 0.088 0.135 Our hexapod 5 0.6 ×0.6 ×0.4 8.8 0.12 / 0.2 0.073 0.064 0.127 0.124 0.095 Abigaille-III 3 0.2 ×0.2 ×0.1 0.6 0.001 0‡0.03 0.03 R-Hex 1 0.5 ×0.4 ×0.1 7.0 0.55 0.175 X-RHex 1 0.6 ×0.4 ×0.1 9.5 1.54 0.175 ASTERISK-H 3 3.4 ? / 0.30 Cassino III 2 0.4 ×0.2 ×0.2 0.02 / 0.15 †The second number indicates the speed when using the wheels. ‡Coxa and femur joints are united. Payload capacity is also an issue with walking robots. Smaller robots have limited payload capacity and effective range, while large robots are slow and inefficient [ 2 ]. Due to the higher energy consumption during movement, walking robots also have a significantly shorter operating time, compared to wheeled or tracked robots, especially on flat terrain. Some research has investigated leg–wheel robots, since wheeled locomotion is faster and less energy demanding on flat terrain, namely, LEON—a hexapod robot that can fold two of its limbs to transform them into wheels [ 14 ], ASTERISK-H—a hexapod robot with a hexagonal body shape and four degrees of freedom per leg [ 15 ], Hylos—a four-legged robot [ 16 ] or Cassino Hexapod III—a hybrid wheeled–legged mobile robot [ 17 ]. However, the increase in speed on flat terrain is usually at the expense of the ability to negotiate difficult or sloping terrain. By analyzing the reported designs, we proposed a novel robot that is capable of moving on flat terrain with low energy consumption, but is also capable of moving on sloping terrain. The robot has a bio-inspired limb structure with five degrees of freedom and, unlike most of the mentioned robots, it is able to move even on very sloping terrain. This is possible because of the presence of a fifth joint—the trochanter, which reduces energy consumption and increases the stability of the robot in sloping terrain. To increase the robot’s endurance on battery, we added an omni-directional wheel to the foot tip (described in more detail in [ 18 ]). This allows the robot to move faster on flat terrain and with lower energy consumption than when using gait [ 17 ]. A prototype was built for experimental verification of the above robot properties. The maximum speed of the robot is 0.12 m/s when using gait and 0.2 m/s when using wheels. The robot is able to walk up to an inclination of 32 ° , to ride inclined terrains up to 40 ° and remain statically stable on slopes up to 50°. The remainder of the paper is organized as follows. The structure of the insect limb is explained and the design of the leg and its kinematic model is introduced in Section 2. The robot movement controller is described in Section 3. The parameters and description of the experiments are presented in Section 4. The results of the experiments are reported in Section 5and discussed in Section 6. Section 7concludes the paper and outlines future work. Robotics 2023,12, 42 3 of 15 2. Leg and Body Design The design of the leg is inspired by insect leg structure so the robot can mimic insect movement patterns. The insect leg consists of five main parts—coxa, trochanter, femur, tibia and tarsus [ 19 ]. The insect leg structure is shown in Figure 1. The coxa part is usually less than 10% of the total leg length and is free to rotate with three degrees of freedom within definite limits. The trochanter is even smaller, in the range of 2–8% of the total leg length [ 20 ]. Femur and tibia are usually the same size or femur is longer than tibia [ 21 ]. Tarsus consists of 3 to 7 segments and its length can vary. The position of each joint depends on the leg position. Front legs have typically different joint positions and link sizes compared to middle or hind legs [22]. Figure 1. Insect leg structure. The limb of an insect consists of five parts—coxa, trochanter, femur, tibia and tarsus. Inspired by [23]. Movement of insect leg parts is provided by muscles [ 24 ]. Muscle contraction causes a change in leg position. However, muscles have much higher power to mass ratios compared to electric motors and servos. Furthermore, joints can typically move in multiple degrees of freedom. Electric motors and servos have typically only one degree of freedom. All these aspects must be reflected when designing an artificial insect leg. Some characteristics can be replicated, others must be adjusted. We wanted to get as close as possible to the ratio of the parts of the insect leg. However, we were limited by the dimensions of the servomotors. Another requirement when designing the limb and selecting the proper components was the payload capacity of the robot. The goal was that the robot would be able to carry a load of its own weight. The resulting dimensions of the robot were adjusted to the size of the designed leg. The dimensions of the robot’s body had to ensure that the individual legs were placed far enough apart and could move freely in the defined areas. The robot is 58 cm long, its height ranges from 15.5 cm to 48.5 cm and its width ranges from 23 cm to 96 cm, depending on the current stance. Bio-inspired robots have three basic leg placements inspired by mammals, spiders and reptiles [ 25 ]. Thanks to the design of the legs, our robot is able to use both spider and reptile placements. The leg of our robot consists of five main parts. The design is similar to insect leg structure. The dimensions of the leg parts are in Table 2. The total length of the leg is 483 mm. The coxa part is larger than 10% of the leg length, because the leg needs to rotate in a full 180 degrees radius. The trochanter is also beyond the expected size, because the joint requires a stronger servomotor, with large dimensions. Femur and tibia parts are the Robotics 2023,12, 42 4 of 15 longest parts of the leg as they should be. Tarsus length can be adjusted as needed. The scheme of the leg is in Figure 2. Table 2. Dimensions of the robot leg. The table shows the dimensions of each part of the robot leg and the models of motors used for each joint. The whole limb measures 483 mm. Part Length [mm] % of the Total Leg Length Dynamixel Servomotor coxa 73 15.11 MX-64 trochanter 64 13.25 MX-106 femur 127 26.29 MX-106 tibia 124 25.67 MX-64 tarsus 95 19.67 MX-64 Figure 2. Robot leg structure. The leg has five Dynamixel servomotors. Each servomotor operates one joint. The servomotors are powered and controlled using a combined bus that chains the servomotors together and provides both power and serial line interconnection. Each joint is operated by one Dynamixel servomotor (see Table 2for details) [ 26 ]. Trochanter and femur joints require the most power compared to other joints, so the MX106 servomotors were used. Coxa, tibia and tarsus joints do not require as much power as trochanter and femur joints, so the MX-64 servomotors were used. Both servomotor types have the same nominal voltage of 12 V and can be powered by a power supply or a battery. Most hexapod robots have only three leg parts and, thus, only three degrees of freedom—coxa, femur and tibia. Although, three joints are enough for fluent walk, the additional joints can be used for various tasks, such as object manipulation. A robot with more degrees of freedom can also move in more stances than a hexapod with three degrees of freedom, which increases the ability of the robot to avoid obstacles or traverse rough terrain. The trochanter joint is the most uncommon joint for hexapod robots, even though it can be used for better stabilization on inclined terrains. The leg can be rotated and positioned parallel to the gravitational force which takes load from the coxa joint and reduces its energy consumption. This situation is shown in Figure 3. Figure 3. Usage of trochanter joint on inclined terrain. ( a ) Our hexapod robot uses trochanter joints on sloping terrain. The leg is set in parallel to the gravitational force. ( b ) Common hexapod without trochanter joint. The gravitational force adds load to the coxa joint. Robotics 2023,12, 42 5 of 15 2.1. Forward Kinematics The forward kinematics of the leg is based on the Denavit–Hartenberg (DH) convention (the Denavit–Hartenberg leg parameters are shown in Table 3). The transformation matrix DH between the coordinate systems of adjacent legs is given by Equation (1): Hi i+1=    cθi−sθicαisθisαiaicθi sθicθicαi−cθisαiaisθi 0sαicαidi 0 0 0 1     (1) where sx denotes sin(x) , cx denotes cos(x) and the DH parameters θi , di , ai and αi are the rotation around z , translation along z , translation along x and rotation around x , respectively. The mapping between the global coordinate system and the foot tip coordinate system is given by Equation (2): Hf 1=H1 2H2 3H3 4H4 5H5 f(2) where fis the foot tip frame. Table 3. Values of the Denavit–Hartenberg parameters of the leg. Link i diaiαiθi [mm] [mm] [rad] [rad] coxa 1 65 0 π/2 θ1 trochanter 2 22 0 π/2 θ2+π/2 femur 3 0 127 0 θ3 tibia 4 0 124 0 θ4 tarsus 5 0 95 0 θ5 2.2. Inverse Kinematics The inverse kinematics task is to find joint angles θl={θ1,θ2,θ3,θ4,θ5} based on the position of the foot tip for all legs l . Due to the five degrees of freedom the solution is under-determined. One solution is to add a constraint as in [ 9 ]. However, we preferred the reduction of controlled degrees of freedom of the leg. The control of the trochanter joint is based on data from the inertial measurement unit, which senses the tilt of the robot’s body, and the tarsus joint is controlled by the reflexive layer that keeps the joint parallel to the gravitational force. The resulting system has only three degrees of freedom. The inverse kinematics can then be solved using the following Equations (3)–(10). The established coordinate system is shown in Figure 4. L=qx2 f+z2 f(3) Lt=q(L−d1)2+y2 f(4) γ=arctan L−d1 yf!(5) β=arccos a2 4−a2 3−L2 t −2a3Lt!(6) α=arccos L2 t−a2 3−a2 4 −2a3a4!(7) θ1=arctan zf xf!(8) Robotics 2023,12, 42 6 of 15 θ3=90 −(γ+β)(9) θ4=90 −α(10) where xf , yf and zf are the foot tip coordinates, d1 is coxa length, a3 is femur length, a4 is tibia length, L is the distance between coxa joint and the foot tip, Lt is the distance between femur joint and the foot tip and θ1 , θ3 and θ4 are the angles for coxa, femur and tibia joints. Figure 4. The leg coordinate system established for the purposes of inverse kinematic calculations. d1 is coxa length, a3 is femur length, a4 is tibia length, L is the distance between coxa joint and the foot tip, Lt is the distance between femur joint and the foot tip, θ1 , θ3 and θ4 are the angles for coxa, femur and tibia joints, α , β and γ are angles used during inverse kinematic calculations and xf , yf and zf are the foot tip coordinates. Both trochanter and tarsus joints are controlled by a reflexive layer and are, thus, not included in the inverse kinematic calculations. Inspired by [27]. 3. Robot Locomotion When planning the robot’s movement, an important aspect is its stability. A legged robot can be in two different states of stability—dynamic or static. A statically-stable robot is in a stable position at every moment of its motion, which means that its center of gravity must be located in the polygon formed by the legs that are currently providing support. A statically-unstable robot is not in a stable position at every moment of its motion. This can be expressed as the center of gravity being outside the polygon of the supporting legs, which means the robot is basically falling. Between these two stability states, there is a critically stable position where the robot balances between the previous two states (see Figure 5). However, a statically-unstable robot can become dynamically stable if additional force is supplied, e.g., by moving a leg [28,29]. The selection of the appropriate gait depends on the desired performance characteristics, such as speed, stability or power consumption, but also on the size and shape of the robot or the complexity of the terrain [17]. There are several indices for comparing walking robots of different sizes, shapes and masses. One of them is the duty factor [ 30 ], which is defined by Equation (11). Duty factor can also be used to distinguish between running and walking, where β< 0.5 is for running and β≥0.5 is for walking [25]. β=support period cycle time (11) where support time is time when the leg provides support and cycle period is duration of one step. The most commonly used gaits can be seen in insects, such as tripod, wave or ripple [ 31 ]. The tripod gait is one of the fastest gaits. It is a regular, periodic gait, where Robotics 2023,12, 42 7 of 15 β= 0.5, which is on the border of running [ 25 ]. The tripod is the most suitable gait for use on flat terrain because it is fast but has relatively low stability. In contrast, the wave is the most stable gait because only one leg is moving at any given time ( β= 5 / 6). It is also the slowest gait. The ripple gait allows movement at medium speed while maintaining relatively high stability. A maximum of two legs are moving at the same time. Figure 5. Robot stability during movement. The supporting leg is shown in black, X represents the robot’s center of gravity. ( a ) The statically-stable robot has a centre of gravity inside a polygon formed by the supporting legs. ( b ) A statically-unstable robot does not have a center of gravity inside the polygon formed by the supporting legs and, thus, the robot is in danger of falling. ( c ) The robot balances at the edge of stability, which is expressed by the centre of gravity at the edge of the polygon formed by the supporting legs. The figure is inspired by [32]. Movement Controller The movement controller adapts the used gait to the current terrain conditions. It consists of five main blocks—reflexive layer, terrain controller, gait selector, leg coordinator and leg controllers (see Figure 6). The controller was described in detail in previous work [18]. Figure 6. Control flow chart of the robot controller. Sensors provide data to the reflexive layer, that can control leg movement directly in case of reflex activation. Sensor data is also sent to the terrain controller, where the data are transformed and used by the gait selector to determine the most appropriate gait for the current terrain. The chosen gait is executed by the leg coordinator, which controls the leg controllers. Robotics 2023,12, 42 8 of 15 Sensor data are processed by the reflexive layer, which, eventually, triggers the reflexive behavior of the robot by sending direct commands to the leg controller. Unless one of the reflexes is activated, data from the sensors is sent to the terrain controller, which analyzes the roughness of the terrain. The most suitable gait is then selected by the gait selector based on the terrain analysis. The resulting gait is obtained by the leg coordinator and executed by the leg controllers. The reflexive layer triggers three reflexes [ 13 ]. The stepping reflex moves the leg closer to the body, reducing energy consumption and increasing the stability of the robot. The elevator reflex is triggered when the leg encounters an obstacle during its movements, whereby it tries to repeat the movement with an increased step height. The search reflex is activated if the leg does not find the support at the expected location. It searches for another support in the surrounding area. 4. Materials and Methods To verify the proposed robot and controller design, a series of experiments were performed. The movement speed and energy consumption were tested using tripod gait and all six wheels, on both flat and sloping terrain. The inclined terrain was simulated by a wooden board with an adjustable slope. The robot was powered by a 12 V power supply. The servomotors were controlled by an U2D2 controller [ 33 ]. The load on the individual servomotors was measured as the current flowing through the servomotor. The actual current of each servomotor was read from the servomotor registers. Another way to measure the load on the servomotors would be the usage of an external current sensor. However, one sensor would need to be attached to each servomotor, which would be very complicated. In addition, the servomotors themselves measure their current with a resolution of 3.36 mA, which was sufficient accuracy for the experiment. The total current of the robot was measured at 50 Hz using a hall effect-based linear current sensor, ACS712, which was connected to the Arduino Mega board. 4.1. Reading Data from Servomotors The servomotors used for the individual robot joints are controlled by TTL half duplex asynchronous serial communication, which is implemented over a single wire [ 34 ]. Its baud rate can be set from 8000 bps to 4.5 Mbps. The 1 Mbps speed was eventually chosen, because higher speeds caused a high number of communication errors. Protocol version 2.0 was used for communication. Unlike the protocol version 1.0, it has the possibility to read or write to multiple servomotors simultaneously using the sync read and sync write methods [ 35 ]. Sync methods allow the reading of data from several servomotors by sending one instruction packet. Each servomotor responds with a status packet. The use of the sync read method reduces the traffic on the communication link. Values can, thus, be read more frequently than with sequential reading. When using a higher baud rate, it is also necessary to reduce the latency of the USB port. We set the USB port latency to 1 ms. The bus speed is also affected by the response time of the individual servomotors [ 36 ]. The response time can be set in the Return Delay Time register. The default value was 250 µ s. This value was reduced up to 20 µ s. Furthermore, the Profile Acceleration register value was set to 20, the Profile Velocity register value was set to 5000 and the Position P Gain register value was set to 850. These modifications increased the smoothness of movement of the individual servomotors and, thus, the movement smoothness and stability of the whole robot. 4.2. Speed and Power Consumption on Sloping Terrain The goal in this experiment was to analyze the power consumption of the servomotors in different stances and movements and to verify that the trochanter joint reduces the load on the other joints when the robot is standing, walking and riding on inclined terrain. Three different static stances and two movements (tripod gait with a maximum speed of 0.12 m/s and a period of 1.6 s and ride using six wheels with a maximum speed of Robotics 2023,12, 42 9 of 15 0.2 m/s) were tested at six different inclinations (see Table 4). All tested stances were based on the robot’s default stance (Figure 7a). The first derived stance (No. 1) did not use the trochanter joint and all limbs were at the same height (Figure 7b). The second derived stance (No. 2) also did not use the trochanter joint, but the individual limbs were at different heights that corresponded to the slope of the tested terrain (Figure 7c). Finally, the third derived stance (No. 3) used the trochanter joint and all limbs were at the same height. The angle of rotation of the trochanter joint was identical to the slope of the tested terrain (Figure 7d). Table 4. The parameters of the proposed experiments. This table describes the parameters of each experiment, specifically the slope of the terrain, the stance used and its characteristics. Each experiment was performed for static stance, walking using tripod gait and driving all six wheels. Terrain Slope [°] Stance Number Trochanter Joint Angle [°] Limbs Posture 01†0 same height 14 1 0 same height 14 2 0 different height 14 3 14 same height 23 1 0 same height 23 2 0 different height 23 3 23 same height 32 1 0 same height 32 2 0 different height 32 3 32 same height 40 1 0 same height 40 2 0 different height 40 3 40 same height 50 1 0 same height 50 2 0 different height 50 3 50 same height † In terrain with zero slope, there was no point in testing the other two stances because they corresponded to stance number 1. Figure 7. Robot stances. ( a ) The default stance. ( b ) The trochanter joint is not used and the legs have the same height. ( c ) The trochanter joint is not used, but the leg height is adjusted according to the slope. (d) The angle of rotation of the trochanter joint is adjusted to the slope of the tested terrain.